Boundary Layer and separation

1
Boundary Layer and separation
Flow decelerates
Flow accelerates
Constant flow
Flow reversal free shear layer highly unstable
Separation point
2
Flow Separation
Separation
Boundary layer
q
Wake
Inviscid curve
Stagnation point
1.0
Turbulent Laminar
0
-1.0
-2.0
-3.0
q
3
Drag Coefficient CD
Stokes Flow, Relt1
Supercritical flow turbulent B.L.
Relatively constant CD
4
Local Heat Transfer Distribution
Stagnation point
qqh(q)(Ts-T?), Nuqh(q)D/kf
Laminar to turbulent transition
Turbulent B.L. growth
q
Turbulent separation
Local Nusselt number for airflow normal to
a circular cylinder. (figure 10-22 from the ITHT
text)
Laminar B.L. growth
separation
5
Averaged Nusselt Number Correlations of
Cylinders in Cross Flows
Note 1 averaged Nusselt number correlations for
the circular cylinder flows can be found in
chapter 10-5. Correlations for other
noncircular cylinders in cross flow can also be
found in this chapter (see Table 10-3). Note 2
Heat transfer between a tube bank (tube bundle)
and cross flow is given in many HT textbooks (for
example see chapter 7 of Introduction to Heat
Transfer by Incropera DeWitt. The
configuration is important for many practical
applications, for example, the multiple pass heat
exchanger in a condenser unit. The use of tube
bank can not only save the operating space but
also can enhance heat transfer. The wake flows
behind each row of tubes are highly turbulent and
can greatly enhance the convective heat transfer.
In general, one can find an averaged convection
coefficient using empirical correlation. Note 3
Because of its compactness, pressure drop across
a tube bank can be also significant and warrants
careful design consideration.
6
Example
A hot-wire anemometer is a flow device used to
measure flow velocity based on the principle of
convective heat transfer. Electric current is
passing through a thin cylindrical wire to heat
it up to a high temperature, that is why it is
called hot-wire. Heat is dissipated to the
fluid flowing the wire by convection heat
transfer such that the wire can be maintained at
a constant temperature. Determine the velocity
of the airstream (it is known to be higher than
40 m/s and has a temperature of 25C), if a wire
of 0.02 mm diameter achieved a constant
temperature of 150C while dissipating 50 W per
meter of electric energy.
25C, Ugt40 m/s
Hot-wire, 0.02 mm dia.
Air (87.5C), Pr0.707, n15?10-6 m2/s, k0.026
W/m.K
Constant temperature 150C
7
Example (cont.)